The electroosmotic flow of viscoelastic fluids is studied analytically by using the Phan-Thien Tannar (PTT) constitutive model. Unidirectional steady-state flow is formed in a two-dimensional microchannel bounded by two parallel plates with different zeta potentials or by a plane substrate and a free surface. The exact flow field is obtained based on first principles. Velocity profiles and flow rates are studied parametrically by varying relaxation time, extensibility parameter and slip parameter of the PTT model and the electrochemical properties of the liquid and the bounding plates. Comparisons are made with Newtonian fluids and previous non-Newtonian analyses. (C) 2012 Elsevier B.V. All rights reserved.